Hans Aberg:
| You say that a pawn ahead is always a win with only some 
| exceptions. So is a rook. So set values of these the same - 
| does not work to predict generic rook against pawn end-games.
You seem to attach a variable meaning to the phrase 'a pawn ahead', so
that I no longer know if you are referring to KPK, or just any position.
The rule of thump amongst Chess players is that in Pawn endings that you
cannot recognize as obvious theoretical wins/draws/losses (like all KPK
positons, positions with passers outside the King's square etc.) a Pawn
advantage makes it 90% likely that you will win. In a Rook ending, OTOH, a
single Pawn advantage will be a draw in 90% of the cases.
| 90 % with respect to what: all games, those that GMs, newbies, or a 
| certain computer program play?
You will always be able to find players that will bungle any advantage,
amongst Humans as well as computers. 90% is the limit to which you
converge with increasing quality play. And you converge to it rather
quickly, because Pawn endings aren't that complicated. Players at a level
where 'opposition' and the 'square rule' are familiar concepts will
probably achieve close to this percentage.
| The traditional piece value system does not refer to a statement 
| like: 'this material advantage leads to a win in 90 % of the cases'.
This is because even the weakest players get to learn the piece-value
system, and the weaker they are, the more faithfully they usually adhere
to it. Even 6 year olds get to learn this before they know about castling
and e.p. capture. And to people that can only look 2 ply ahead a Pawn
advantage obviously means a lot less (in terms of score benifit they will
achieve because of this) than to 1900-rated players.

So the win percentage derived from a certain advantage according to the
piece-value system is not fixed. But that is not the same as saying that
for a given level of play, a larger advantage does not result in a higher
score. In fact it does. At any level of play, giving Knight odds between
equal players leads to a much larger win percentage than giving Pawn odds,
while Rook odds would give even more (if by then it would not already be
100%).

But if a certain position (or set of positions characterized by the same
material imbalance, as I use in my test matches) would be won in 90% of
the cases between equal players at any level above 1800 Elo by white (but
tail off below that, when you get into the regions of the real patzers),
would it, according to your definition, still be possible that black
actually had the better 'winning chances'? And that a piece-value system
that would predict these better 'winning chances' for black thus was a
correct and viable system?

I would prefer (and advice anyone else) to use a piece-value system that
would actually predict that white had better winning chances in that
position! As, by the time you will have gone through the trouble of
forcing the opponent to this position, selected on basis of the system,
you will be subjected to these very same winning chances.